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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.comparisons"></a><a class="link" href="comparisons.html" title="Comparisons to Other Open Source Libraries">Comparisons to Other Open Source
    Libraries</a>
</h2></div></div></div>
<p>
      We've run our performance tests both for our own code, and against other open
      source implementations of the same functions. The results are presented below
      to give you a rough idea of how they all compare. In order to give a more-or-less
      level playing field our test data was screened against all the libraries being
      tested, and any unsupported domains removed, likewise for any test cases that
      gave large errors or unexpected non-finite values.
    </p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../doc/src/images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top"><p>
        You should exercise extreme caution when interpreting these results, relative
        performance may vary by platform, by compiler options settings, the tests
        use data that gives good code coverage of <span class="emphasis"><em>our</em></span> code,
        but which may skew the results towards the corner cases. Finally, remember
        that different libraries make different choices with regard to performance
        verses numerical stability.
      </p></td></tr>
</table></div>
<p>
      The first results compare standard library functions to Boost equivalents with
      MSVC-14.0:
    </p>
<div class="table">
<a name="math_toolkit.comparisons.table_Library_Comparison_with_Microsoft_Visual_C_version_14_2_on_Windows_x64"></a><p class="title"><b>Table 23.14. Library Comparison with Microsoft Visual C++ version 14.2 on Windows
      x64</b></p>
<div class="table-contents"><table class="table" summary="Library Comparison with Microsoft Visual C++ version 14.2 on Windows
      x64">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                boost 1.73
              </p>
            </th>
<th>
              <p>
                math.h
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                cbrt<br> (85/85 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (62ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j (integer order)<br> (267/268 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (123ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (185ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann (integer order)<br> (428/428 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.01<br> (158ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (156ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erf<br> (950/950 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.15<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erfc<br> (950/950 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (54ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (59ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expm1<br> (80/80 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.10<br> (11ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (10ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                lgamma<br> (400/400 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (80ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (128ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                log1p<br> (80/80 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (14ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (15ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma<br> (400/400 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (74ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">12.53<br> (927ns)</span>
              </p>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
      On Linux with GCC, we can also compare to the TR1 functions, and to GSL and
      RMath:
    </p>
<div class="table">
<a name="math_toolkit.comparisons.table_Library_Comparison_with_GNU_C_version_9_2_1_20191008_on_linux"></a><p class="title"><b>Table 23.15. Library Comparison with GNU C++ version 9.2.1 20191008 on linux</b></p>
<div class="table-contents"><table class="table" summary="Library Comparison with GNU C++ version 9.2.1 20191008 on linux">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                boost 1.73
              </p>
            </th>
<th>
              <p>
                boost 1.73<br> promote_double&lt;false&gt;
              </p>
            </th>
<th>
              <p>
                tr1/cmath
              </p>
            </th>
<th>
              <p>
                GSL 2.5
              </p>
            </th>
<th>
              <p>
                Rmath 3.6.3
              </p>
            </th>
<th>
              <p>
                math.h
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                assoc_laguerre<br> (2240/2240 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (156ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (143ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (148ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (166ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                assoc_legendre<br> (110/400 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.75<br> (279ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.75<br> (171ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (36ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.25<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta (incomplete)<br> (2682/3210 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.96<br> (2076ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (524ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.20<br> (628ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta<br> (2203/2204 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.51<br> (789ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (145ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.14<br> (330ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.27<br> (238ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cbrt<br> (85/85 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.32<br> (58ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (32ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (31ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i (integer order)<br> (494/526 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.76<br> (767ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (174ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (161ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (295ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.25<br> (845ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i<br> (177/240 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.12<br> (1182ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (239ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (166ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.14<br> (688ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.92<br> (1315ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j (integer order)<br> (251/268 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.95<br> (319ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (108ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.19<br> (237ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (187ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.59<br> (388ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.39<br> (150ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j<br> (433/451 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.16<br> (1067ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (359ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (338ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (558ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (368ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k (integer order)<br> (505/508 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">18.17<br> (3289ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (181ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">9.73<br> (1761ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.10<br> (200ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (238ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k<br> (96/279 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">10.37<br> (3962ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (382ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (700ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (389ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (416ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann (integer order)<br> (424/428 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.71<br> (466ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (172ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.95<br> (679ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.03<br> (522ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.05<br> (869ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (225ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann<br> (428/450 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">14.08<br> (8826ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.68<br> (4814ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (757ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (789ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (627ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                digamma<br> (1019/1019 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.77<br> (62ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.97<br> (104ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.20<br> (217ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1 (complete)<br> (109/109 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.48<br> (93ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (63ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.56<br> (98ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.03<br> (191ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1<br> (627/629 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.01<br> (310ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (154ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (191ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.13<br> (328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2 (complete)<br> (109/110 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (44ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">8.76<br> (219ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">15.24<br> (381ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2<br> (527/530 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.98<br> (704ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (236ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (294ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.15<br> (507ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3 (complete)<br> (0/500 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3<br> (22/845 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.52<br> (609ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (217ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (173ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (235ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rc<br> (201/201 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.13<br> (66ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (31ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.03<br> (156ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rd<br> (7588/7588 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.34<br> (428ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (128ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.88<br> (240ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rf<br> (7788/7788 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.71<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (49ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.65<br> (228ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rj<br> (7642/8032 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.04<br> (426ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (140ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">10.84<br> (1518ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erf<br> (950/950 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.71<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.21<br> (101ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (24ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erfc<br> (950/950 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.18<br> (89ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.32<br> (65ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.32<br> (93ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (28ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint (En)<br> (1059/1059 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.12<br> (242ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (114ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.86<br> (440ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint<br> (436/436 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.02<br> (85ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.60<br> (109ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.10<br> (172ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expm1<br> (80/80 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (16ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (16ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (17ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p<br> (1379/1379 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.64<br> (618ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (260ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.79<br> (420ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (234ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p_inv<br> (559/559 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.24<br> (2328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1038ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (1211ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q<br> (1371/1379 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.59<br> (629ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (253ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.02<br> (492ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (243ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q_inv<br> (78/559 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.57<br> (2016ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (958ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (783ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta<br> (3210/3210 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.33<br> (1979ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (524ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (371ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta_inv<br> (1204/1210 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.92<br> (5552ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1902ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.73<br> (5188ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac<br> (3210/3210 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.44<br> (2008ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (590ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (452ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac_inv<br> (1201/1210 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.99<br> (5533ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1853ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.43<br> (4504ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_cn<br> (2368/2757 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.00<br> (483ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.36<br> (163ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_dn<br> (2368/2757 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.19<br> (503ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.47<br> (173ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (70ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_sn<br> (2368/2757 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">6.20<br> (614ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.82<br> (180ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (99ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                laguerre<br> (280/280 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (92ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.10<br> (99ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (134ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre Q<br> (300/300 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (390ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (314ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (340ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre<br> (300/300 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (282ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (251ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (290ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                lgamma<br> (400/400 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.30<br> (265ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.34<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (52ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.08<br> (204ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.08<br> (104ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (50ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                log1p<br> (80/80 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.18<br> (20ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (22ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (17ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (17ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                polygamma<br> (823/1535 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">23.31<br> (8883ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.98<br> (756ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (598ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (381ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_bessel<br> (483/483 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.91<br> (1122ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (588ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.14<br> (1844ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.96<br> (1155ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_neumann<br> (284/284 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.16<br> (2842ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.56<br> (1015ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.44<br> (2953ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (397ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma (incomplete)<br> (1266/1379 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.90<br> (669ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (231ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.19<br> (505ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma<br> (400/400 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.10<br> (472ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (144ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.33<br> (153ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (118ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (115ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (180ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                trigamma<br> (659/659 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.08<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (12ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">53.75<br> (645ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">30.92<br> (371ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                zeta<br> (448/448 tests selected)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.21<br> (455ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (108ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">1078.95<br> (116527ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.03<br> (219ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p>
      And finally we can compare the statistical distributions to GSL, RMath and
      DCDFLIB:
    </p>
<div class="table">
<a name="math_toolkit.comparisons.table_Distribution_performance_comparison_with_GNU_C_version_9_2_1_20191008_on_linux"></a><p class="title"><b>Table 23.16. Distribution performance comparison with GNU C++ version 9.2.1 20191008
      on linux</b></p>
<div class="table-contents"><table class="table" summary="Distribution performance comparison with GNU C++ version 9.2.1 20191008
      on linux">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                boost 1.73
              </p>
            </th>
<th>
              <p>
                Boost<br> promote_double&lt;false&gt;
              </p>
            </th>
<th>
              <p>
                GSL
              </p>
            </th>
<th>
              <p>
                Rmath 3.6.3
              </p>
            </th>
<th>
              <p>
                DCDFLIB
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                ArcSine (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (33ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ArcSine (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ArcSine (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.14<br> (437ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (139ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.24<br> (450ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.94<br> (269ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.52<br> (350ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.50<br> (360ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (103ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.31<br> (238ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.61<br> (2587ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (991ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">14.97<br> (14833ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (1809ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.24<br> (7178ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.58<br> (837ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (324ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.16<br> (701ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (484ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (536ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.66<br> (322ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (121ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (222ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.96<br> (3917ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (1548ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1323ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.59<br> (8716ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (36ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (36ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.67<br> (17ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (45ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (48ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">75.60<br> (3402ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.93<br> (87ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">6.00<br> (1002ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.03<br> (506ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">9.54<br> (1593ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.46<br> (243ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (167ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.43<br> (295ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (110ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.04<br> (1664ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (815ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">18.96<br> (15454ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.84<br> (1501ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.40<br> (5220ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.47<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (32ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.84<br> (35ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (30ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (47ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.13<br> (26ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.48<br> (34ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (36ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (57ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (58ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (85ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (53ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (51ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                F (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.83<br> (817ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (289ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.52<br> (729ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (399ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.51<br> (436ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                F (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.87<br> (361ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (126ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (156ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                F (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.11<br> (2615ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1241ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">11.07<br> (13741ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.09<br> (2589ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.32<br> (6604ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.10<br> (714ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.53<br> (267ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.93<br> (684ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (248ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (174ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.87<br> (437ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (113ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (153ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.83<br> (1827ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (755ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">11.04<br> (7119ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.25<br> (1454ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (645ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.12<br> (53ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.32<br> (58ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">15.78<br> (363ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.88<br> (72ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">95.49<br> (66745ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">88.59<br> (61922ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (699ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (729ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">141.15<br> (73824ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">121.97<br> (63790ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (523ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (131293ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.75<br> (166268ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (95222ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.92<br> (1538ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (803ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.72<br> (367ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (135ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (2328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1322ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.25<br> (806ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (359ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.41<br> (515ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (151ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.37<br> (2187ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (921ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (236ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (242ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3530ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (3823ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.20<br> (49ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (43ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (39ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (40ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (42ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.14<br> (225ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.34<br> (141ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (120ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (74ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (76ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (74ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (101ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (78ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (80ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (71ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (47ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (46ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (44ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.66<br> (1354ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (540ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.91<br> (974ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (509ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (589ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.40<br> (445ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (131ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.45<br> (190ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.56<br> (7468ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (2918ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.97<br> (8664ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.91<br> (11414ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.71<br> (2083ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (769ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (976ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.48<br> (1265ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (511ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.13<br> (578ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.90<br> (55809ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (19273ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.91<br> (75343ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">9.11<br> (4498ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.71<br> (2821ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">18.21<br> (8997ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (494ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.05<br> (953ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (436ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (312ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.54<br> (31465ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (17712ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">34.65<br> (428458ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (12366ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.74<br> (1828ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (667ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.74<br> (1160ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.66<br> (1104ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.73<br> (1506ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (564ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (551ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.88<br> (29414ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (10228ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.53<br> (56602ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.34<br> (13703ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.62<br> (6416ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.09<br> (2907ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1389ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.77<br> (4034ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (2284ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (2898ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.33<br> (68590ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (29386ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.29<br> (67338ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.59<br> (150ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (58ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (87ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.12<br> (181ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (34ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (33ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (51ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (57ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (40ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (52ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (40ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">13.10<br> (524ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (49ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (52ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (86ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (52ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (63ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.16<br> (264ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (122ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.03<br> (370ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.70<br> (207ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (155ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.73<br> (218ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (80ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.54<br> (123ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.22<br> (1193ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.01<br> (540ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (537ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.49<br> (2409ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.39<br> (32ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (36ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.37<br> (37ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (691ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (633ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.58<br> (174ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (110ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (6788ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5813ns)</span>
              </p>
            </td>
<td>
            </td>
<td>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">6.46<br> (1893ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.24<br> (656ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (293ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (303ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (367ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.36<br> (724ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (176ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (135ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.62<br> (2959ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (954ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (986ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (818ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.45<br> (2822ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.10<br> (76ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (81ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="grey">-</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (92ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (74ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (77ns)</span>
              </p>
            </td>
<td>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div>
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